Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and efficient representation for the strapdown inertial navigation system (INS). The current work is motivated by simplifying the existing dual quaternion representation of the kinematic model. This paper proposes a compact and elegant representation of the body's attitude, velocity and position, with the aid of a devised trident quaternion tool in which the position is accounted for by adding a second imaginary part to the dual quaternion. Eventually, the kinematics of strapdown INS are cohesively unified in one concise differential equation, which bears the same form as the classical attitude quaternion equation. In addition, the computation of this trident quaternion-based kinematic equation is implemented with the recently proposed functional iterative integration approach. Numerical results verify the analysis and show that incorporating the new representation into the functional iterative integration scheme achieves high inertial navigation computation accuracy as well.

中文翻译：

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基于惯性导航的三叉戟四元数框架第一部分：刚性运动表示和计算

捷联惯性导航研究涉及在选定参考系中对刚体的姿态，速度和位置进行参数化和计算。社区一直致力于为捷联惯性导航系统（INS）找到最简洁，最有效的表示形式。通过简化运动学模型的现有双四元数表示法来推动当前的工作。本文借助设计的三叉戟四元数工具提出了一种简洁，优雅的身体姿态，速度和位置表示方法，该工具通过在双四元数上增加第二个虚部来说明位置。最终，捷联惯性运动学在一个简洁的微分方程中紧密地统一在一起，其形式与经典的姿态四元数方程相同。另外，利用最近提出的功能迭代积分方法实现了基于三叉戟四元数的运动学方程的计算。数值结果验证了分析结果，表明将新的表示法引入功能迭代积分方案中也可以实现较高的惯性导航计算精度。